Loss of the animal only counts against a bag limit if you get caught. Which is why nothing happens.Loss of the animal would count against your bag limit. But that's irrelevant too if a 223 will kill a bear. It does probably more times a year than any other cartridge.
It's totally relevant unless it always kills the bear. Does it always kill them?
One thing to shoot and kill a bear from a safe distance, under safe conditions, with a pea-shooter. Another to stop a charging bear before it mauls or kills the shooter/hunter. Most hunters want a cartridge that will stop them quickly in both scenarios. Don't care how many bear kills you have, how many your friends have, how many the Alaska natives you know claim to have, how many stories you've heard of 223 bear kills, or how many times you repeat yourself. 223s won't stop/disable a bear given the wide variety of shot conditions experienced when hunting wild bears, as quickly as the 30, 338, 375, 416, 458 magnum class of cartridges. Your insistence that 223s can and do kill bears is accepted. Any insistence that 223s will stop a big determined black, grizzly, or brown as quickly and reliably as the larger caliber magnum cartridges in most common use by bear guides, and most bear hunters hunting on foot, is silly nonsense.
Alaska natives do a lot of hunting from snow machines, ATVs, and boats. Caribou, moose, bears, and wolves. Not many roads extend from the remote native villages to their hunting grounds. I'd feel pretty safe bear hunting with a pea shooter too, as long as the engine was running or left idling.
I can say the 223 probably doesn't kill bear more times a year than any other cartridge, and it means as much as your "does probably". Both statements include the word probably, and are equally baseless.